Cardinals stater Michael Wacha was lifted after walking Rene Rivera and pinch-hitter Tommy La Stella greeted reliever Matt Bowman with a run-scoring double to left-center that made it 5-1.
After Jedd Gyorko led off with a walk, Jose Martinez singled up the middle and Paul DeJong followed with a looping base hit just out of the reach of Cubs shortstop Addison Russell to make it 1-0.
The Cubs (88-69) enter Wednesday's action with a magic number of 1, needing a win _ or a Milwaukee loss _ will give the defending World Series champs their second consecutive division crown.
For the Cubs, Rene Rivera replaces Willson Contreras behind the plate, with Baez back at second after missing most of Tuesday's game after fouling a ball of his knee on Monday night.
Rodriguez, 44, has been with the organization 10 years, directing the Cardinals' amateur scouting efforts overseas and supervising the player development and facility operations at the team's Dominican Republic Academy.
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